What is the integral from-pi to 0 of sin^2(x) ?

The integral from-pi to 0 of sin^2(x) is pi/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-pi to 0 of sin^2(x)

\int_{- π}^{0} sin^{2} (x) d x

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

\int_{- π}^{0} sin^{2} (x) d x

Rewrite using trig identities

= \int_{- π}^{0} \frac{1 - cos ( 2 x )}{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int_{- π}^{0} 1 - cos (2 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int_{- π}^{0} 1 d x - \int_{- π}^{0} cos (2 x) d x)

\int_{- π}^{0} 1 d x = π

\int_{- π}^{0} cos (2 x) d x = 0

= \frac{1}{2} (π - 0)

Simplify

\frac{1}{2} (π - 0) : \frac{π}{2}

= \frac{π}{2}

What is the integral from-pi to 0 of sin^2(x) ?
The integral from-pi to 0 of sin^2(x) is pi/2